1. Field of the Invention
The invention relates generally to optical communication systems and, more particularly, to transmission and reception of multilevel optical signals designed to maximize power efficiency in the presence of signal-dependent and signal-independent noises, finite transmitter extinction ratio, and intersymbol interference (ISI).
2. Description of the Related Art
It is well known that in optical communication systems, encoding digital information in multilevel optical signals is more bandwidth-efficient than encoding the information in binary signals. As compared to binary signals, multilevel optical signals have longer symbol duration and have narrower spectra (both in the optical domain and in the electrical domain, after detection at a receiver). These attributes of multilevel signals increase immunity to ISI, increase spectral efficiency in wavelength-division-multiplexed systems, and relax the bandwidth requirements of optical and electrical components in the transmitter, receiver and intervening optical transmission medium.
Most practical optical receivers detect the intensity of a received optical signal, typically using direct detection. In this description, we restrict our attention to multilevel signals having at least three distinct intensity levels. The multilevel signals we consider may also have arbitrary phase and/or frequency modulation, whether intentional (e.g., correlative line encoding for spectral narrowing) or unintentional (e.g., due to chirp of a directly modulated transmitter laser).
It is well known that optical communication systems may exhibit various impairments, including several types of signal-dependent noise, several types of signal-independent noise, a finite transmitter extinction ratio, and ISI. When signal-dependent noise is present, typically, higher intensity levels are received with more noise than lower intensity levels. An important example is signal-spontaneous beat noise, whose variance is proportional to received signal intensity. Another common example is transmitter intensity noise, whose variance is proportional to the square of received signal intensity. In the presence of signal-dependent noise, if a transmitted signal has equally spaced intensity levels, at the receiver, decisions at thresholds between higher intensity levels are subject to higher error probability than decisions at thresholds between lower intensity levels. This implies that the use of equally spaced intensity levels does not yield the lowest overall error probability for a given transmitted power or, equivalently, does not permit the lowest transmitted power yielding a desired overall error probability. When signal-dependent noise is present, it is desirable to transmit signals having unequally spaced intensity levels chosen so that the decisions at all thresholds achieve substantially equal error probabilities. This minimizes the overall error probability for a given transmit power or, equivalently, minimizes the transmitted power required to achieve a desired overall error probability. To achieve optimized performance, these intensity levels should be chosen taken account of several key impairments, including signal-dependent noise, signal-independent noise, a finite transmitter extinction ratio, and ISI.
Kinsel in U.S. Pat. No. 3,774,437 described the use of unequally spaced intensity levels to improve performance in the presence of signal-dependent noise, background light and photodetector leakage current, but did not describe how to choose the intensity levels to optimize performance in the face of specific impairments. Uyematsu, Kikuchi and Sakaniwa in a paper entitled xe2x80x9cTrellis Coded Modulation for Multilevel Photon Communication Systemxe2x80x9d presented at ICCS/ISITA in 1992 described the optimal intensity levels for use with 4-ary pulse-amplitude modulation (4-PAM) in the presence of signal shot noise, background light and photodetector leakage current. Walkin and Conradi in a paper entitled xe2x80x9cMultilevel Signaling for Increasing the Reach of 10 Gb/s Lightwave Systemsxe2x80x9d published by the Journal of Lightwave Technology in November, 1999, discussed how to design the optimal intensity levels in a 4-PAM system in two particular cases. First, they described the optimal levels when the only significant impairment is signal-spontaneous beat noise, which has a variance proportional to the intensity. In this case, they did not treat other important impairments, such as other forms of signal-dependent noise, signal-independent noise, finite transmitter extinction ratio, or ISI. Second, they described the optimal levels when the only significant impairments are transmitter intensity noise (which has a variance proportional to the square of the intensity) and finite transmitter extinction ratio. In this case, however, they did not consider other key impairments, including other forms of signal-dependent noise, signal-independent noise, or ISI.
There is a need for methods and apparatus to transmit multilevel optical signals having intensity levels designed taking account of arbitrary admixtures of key impairments, including: one or more types of signal-dependent noises, whose variances exhibit various dependencies on intensity; signal-independent noise; finite transmitter extinction ratio; and ISI. These methods and apparatus should employ analytical and/or numerical techniques to design the levels, as appropriate for the admixture of impairments encountered in a particular system. These methods and apparatus should be usable in conjunction with offline and/or online determination of a system""s impairments. These methods and apparatus should be capable of achieving specified equal or unequal error probabilities at different decision thresholds.
It is therefore an object of the present invention to provide methods and apparatus to transmit multilevel optical signals having intensity levels designed taking account of an admixture of relevant impairments.
Another object of the present invention is to provide methods and apparatus to transmit multilevel optical signals having intensity levels designed to take into account one or more types of signal-dependent noises whose variances exhibit various dependencies on intensity; signal-independent noise; finite transmitter extinction ratio; and ISI.
Another object is to provide methods and apparatus to optimize the intensity levels using analytical and/or numerical techniques, as appropriate for the admixture of impairments encountered in a particular system.
Another object is to provide methods and apparatus to optimize the intensity levels in conjunction with offline and/or online determination of a system""s impairments.
Another object is to provide methods and apparatus to optimize the intensity levels to achieve specified equal or unequal error probabilities at different decision thresholds.
The above objects of the invention, among others, either singly or in combination, are obtained by the present invention, which includes a transmitter that encodes a transmitted information bit stream in a transmitted multilevel optical signal. A multilevel optical signal is an optical signal whose intensity (instantaneous power) is a pulse-amplitude modulation (PAM) signal assuming at least three levels. The transmitted multilevel optical signal has a set of M transmitted intensity levels Pt,k, k=0, . . . , Mxe2x88x921, where Mxe2x89xa73, and is characterized by an extinction ratio parameter xcex4=Pt,0/Pt,Mxe2x88x921. The transmitter launches the transmitted multilevel optical signal into an optical transmission medium, which typically includes optical amplifiers to compensate for loss. A received multilevel optical is received through the optical transmission medium. The received multilevel optical signal has a set of M received intensity levels Pk, k=0, . . . , Mxe2x88x921. The set of received intensity levels is a scaled version of the set of transmitted intensity levels.
The received multilevel optical signal is input to a receiver, which typically includes an optical preamplifier having a gain G to amplify the received optical signal. At the optical preamplifier output, the amplified multilevel optical signal includes amplified spontaneous emission (ASE) from the optical preamplifier and from optical amplifiers in the optical transmission medium. The amplified multilevel optical signal is passed through an optical bandpass filter to band limit the received ASE, and the filter output is incident upon a photodetector having a responsivity R, whose output is a received photocurrent. The received photocurrent is a multilevel signal having a set of M received photocurrent levels Ik, k=0, . . . , Mxe2x88x921; this set is a scaled version of the set of M received intensity levels. The received photocurrent is amplified by an electrical preamplifier, which outputs a multilevel electrical signal having a set of M levels that is a scaled version of the set of M received photocurrent levels. The multilevel electrical signal includes several noise components; when the received multilevel optical signal takes on intensity level Pk and the received photocurrent takes on level Ik, the noise components have a variance (referred to the electrical preamplifier input) "sgr"k2="sgr"ind2+xcex3Pk. The variance includes a signal-independent term "sgr"ind2, which is dominated typically by electronic noise in the electrical preamplifier. The variance also includes a signal-dependent term xcex3Pk, which is dominated typically by a beat term between the received multilevel optical signal and the received ASE.
A multilevel decoder compares the multilevel electrical signal to a set of Mxe2x88x921 thresholds Ith,k=("sgr"kIkxe2x88x921+"sgr"kxe2x88x921Ik)/("sgr"kxe2x88x921+"sgr"k), k=1, . . . Mxe2x88x921, and makes decisions to estimate the transmitted information bit stream. Because of noise, decisions are subject to errors. The error probabilities at the Mxe2x88x921 thresholds are characterized by the set of (Mxe2x88x921) Q factors Qk=(Ikxe2x88x92Ikxe2x88x921)/("sgr"k+"sgr"kxe2x88x921), k=1, . . , Mxe2x88x921.
A set of optimized received intensity levels, which minimize a received average optical power       P    av    =            (              1        M            )        ⁢                  ∑                  k          =          0                          M          -          1                    ⁢              xe2x80x83            ⁢              P        k            
required so that all (Mxe2x88x921) Q factors Qk, k=1, . . . , Mxe2x88x921 achieve a required value Q, is determined by a level-setting algorithm as follows. A parameter describing the relative strength of signal-independent and signal-dependent noises is defined: xcfx81ind="sgr"ind2/xcex3, and a parameter proportional to the required Q factor is defined: C=Q{square root over (xcex3)}/RG. The set of optimized received intensity levels is then determined using:                     P                  M          -          1                    =                                                                                    (                                      M                    -                    1                                    )                                ⁢                                  C                  [                                                                                    (                                                  1                          +                          δ                                                )                                            ⁢                                              (                                                  M                          -                          1                                                )                                            ⁢                      C                                        +                                                                                                                                            2                  ⁢                                                            (                                                                                                                                  ρ                              ind                                                        ⁡                                                          (                                                              1                                -                                δ                                                            )                                                                                2                                                +                                                                                                            δ                              ⁡                                                              (                                                                  M                                  -                                  1                                                                )                                                                                      2                                                    ⁢                                                      C                            2                                                                                              )                                                              1                      2                                                                      ]                                                                          (                          1              -              δ                        )                    2                      ,          and      ⁢              :                                P        k            =                                    (                          kC              +                                                                    ρ                    ind                                    +                                      δ                    ·                                          P                                              M                        -                        1                                                                                                                  )                    2                -                  ρ          ind                      ,          k      =              0        ⁢                  xe2x80x83                ⁢        …              ⁢          xe2x80x83        ,          M      -      2.      
The optimized received intensity levels depend on M, the required Q factor, the relative strength of signal-independent and signal-dependent noises, and the transmitter extinction ratio parameter. The set of optimized received intensity levels is scaled appropriately to obtain a set of optimized transmitted intensity levels.
An advantage of the present invention is that it can optimize the power efficiency of multilevel optical signals taking account of a wide range of system impairments, including: one or more types of signal-dependent noise exhibiting various dependencies on intensity; signal-independent noise; finite transmitter extinction ratio; and ISI.
Another advantage of the present invention is that it optimize the power efficiency of multilevel optical signals to achieve various objectives; specifically, the present invention can minimize the received power required to achieve specified equal or unequal error probabilities at different decision thresholds, or can minimize the error probabilities at different decision thresholds subject to a limit on received power.
Another advantage of the present invention is that it can optimize the power efficiency of multilevel optical signals based on offline or online determination of a system""s impairments.
Another advantage of the present invention is that it improves the power efficiency of multilevel optical signals, yielding several potential benefits, including: an increased transmission distance, an increased system power margin, and a reduced optical power launched into an optical transmission medium, the latter potentially reducing the impact of optical nonlinearities in the optical transmission medium.
Another advantage of the present invention is that it improves the power efficiency of multilevel optical signals, enabling realization of all the attendant advantages of multilevel signals, including a longer symbol duration and a narrower spectrum, thereby increasing immunity to ISI, increasing spectral efficiency in wavelength-division-multiplexed systems, and relaxing bandwidth requirements of optical and electrical components in transmitters, receivers and intervening optical transmission media.